Community detection for networks with unipartite and bipartite structure

Abstract

Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite network consists of one set of nodes and a bipartite network consists of two nonoverlapping sets of nodes with only links joining the nodes in different sets. However, a third type of network exists, defined here as the mixture network. Just like a bipartite network, a mixture network also consists of two sets of nodes, but some nodes may simultaneously belong to two sets, which breaks the nonoverlapping restriction of a bipartite network. The mixture network can be considered as a general case, with unipartite and bipartite networks viewed as its limiting cases. A mixture network can represent not only all the unipartite and bipartite networks, but also a wide range of real-world networks that cannot be properly represented as either unipartite or bipartite networks in fields such as biology and social science. Based on this observation, we first propose a probabilistic model that can find modules in unipartite, bipartite, and mixture networks in a unified framework based on the link community model for a unipartite undirected network [B Ball et al (2011 Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both overlapping and nonoverlapping communities) and apply it to two real-world networks: a southern women bipartite network and a human transcriptional regulatory mixture network. The results suggest that our model performs well for all three types of networks, is competitive with other algorithms for unipartite or bipartite networks, and is applicable to real-world networks.S Online supplementary data available from stacks.iop.org/NJP/16/093001/ mmedia Keywords: community structure, mixture network, probabilistic model, unipartite and bipartite structure 2 New J. Phys. 16 (2014) 093001 C Chang and C Tang drawbacks when used in mixture networks without considering their own characteristics. First, directly using algorithms that can work for bipartite networks, such as biclustering [26] or hierarchical clustering [20], will omit the association between pairs of nodes that are actually one. Such nodes may be partitioned into different modules improperly, even when a community detection algorithm does not allow for an overlapping community or when they are assigned to the same module with two different weights or probabilities. In addition, projecting a mixture network into a unipartite network is an alternative choice [21], but information will be lost in such a process, as it would be for a bipartite network [8,27], and only one vertex set, rather than both, can be assigned to modules following the transformation. Furthermore, imputation methods can be used to convert the second type of mixture networks to unipartite networks by predicting missing values [28]. However, the performance of a community detection algorithm will then depend on the performance of the...

Finding maximal bicliques in bipartite networks using node similarity

“…Almost weak 3 9 10 12 13 14 ; 12 13 14 -10 4 3 5 6 8 ; 1 2 3 4 6 -10 5 8 9 ; 1 3 8 9 10 11 12 13 16 0 Weak 6 2 3 5 6 8 ; 1 2 3 -11 7 5 6 7 8 ;2 3 4 7 -11 8 1 3 5 6 8 ;1 2 4 -10 9 3 5 ; 1 2 3 4 5 6 -7 10 10 12 ; 11 12 13 14 15 -6 11 8 9 10 12 ;11 12 13 -4 12 8 9 10 12 13 14 ; 12 13 -1 Very weak 13 9 11 ; 14 17 18 -14 7 8 9 12 ;10 13 -15 5 7 8 9 ; 3 9 -16 6 8 9 ; 1 3 8 - The results in Table 2 for MaxBic and MaxBicR are very encouraging. The two methods with higher NMI have prematched the ground truth by presetting either the number of communities K = 2 (Chang and Tang 2014) or the maximum number of memberships v = 2 (Gregory 2010), but still don't obtain the ground truth communities. MaxBic and MaxBicR(0.6) outperform BiTector, which also merges maximal bicliques (one of its 4 communities is our community 5 and, similarly, is their only one split across ground truth communities) and linkcomm, the only algorithm based on edge similarity rather than node similarity.…”

Pitman–Yor process mixture model for community structure exploration considering latent interaction patterns*

“…Besides, there exists other community structure in which the links are established less frequently inside the communities than those between the different communities, e.g., transcriptional regulatory networks, shareholding networks, and cooccurring word networks. [12,13] We call the communities with higher external connectivity disassortative community. The diverse community structures bring about numerous community detection methods.…”

“…[6] There are numerous variants based on SBM or modified SBM, for instance, for the assortative community, [21,22] the bipartite community [10,23] and even the disassortative community. [13] However, in order to achieve a higher likelihood in the parameter inference process, the methods based on the SBM are prone to divide a community even if the vertices in this community have similar behaviors. [24] This character sometimes leads to meaningless and unexplainable results.…”

Quantitative function and algorithm for community detection in bipartite networks

“…In addition, several studies have designed algorithms to maximize these modularity functions for community detection in bipartite networks [19-21, 24, 31]. More recently, Chang and Tang proposed a probabilistic model to find modules in unipartite, bipartite, and mixture networks [29].…”